Quantum Wells, Wires and Dots will provide all the essential information, both theoretical and computational, to develop an understanding of the electronic, optical and transport properties of these semiconductor nanostructures. The book will lead the reader through comprehensive explanations and mathematical derivations to the point where they can design semiconductor nanostructures with the required electronic and optical properties for exploitation in these technologies. The first chapters will be concerned with semiconductors and heterostructures and solutions to Schrodinger's equation and numerical solutions. Chapters 4 to 6 will cover diffusion, impurities and excitons. Chapters 7 to 9 will provide information on strained quantum wells, simple models of quantum wires and dots and quantum dots, respectively. Carrier scattering, electron transport, multiband envelope function method, optical waveguiding, introduction to non-linear optical effects, empirical pseudopotential theory and microscopic electronic properties of semiconductor heterostructures will be discussed in Chapters 10 to 16. The final chapter will be on the application of quantum wires and dots.

This text is designed to lead the reader through a series of simple theoretical and computational implementations, and slowly build from solid foundations, to a level where the reader can begin to initiate theoretical investigations or explanations of their own. Aimed at postgraduate students of semiconductor and condensed matter physics, the book is essential to all those researching in academic and industrial laboratories worldwide.

Preface
Acknowledgements
About the authors
About the book
Introduction
Semiconductors and heterostructures
The mechanics of waves
Crystal structure
The effective mass approximation
Band theory
Heterojunctions
Heterostructures
The envelope function approximation
The reciprocal lattice
Solutions to Schrödinger's equation
The infinite well
In-plane dispersion
Density of states
Subband populations
Finite well with constant mass
Effective mass mismatch at heterojunctions
The infinite barrier height and mass limits
Hermiticity and the kinetic energy operator
Alternative kinetic energy operators
Extension to multiple-well systems
The asymmetric single quantum well
Addition of an electric field
The infinite superlattice
The single barrier
The double barrier
Extension to include electric field
Magnetic fields and Landau quantisation
In summary
Numerical solutions
Shooting method
Generalised initial conditions
Practical implementation of the shooting method
Heterojunction boundary conditions
The parabolic potential well
The Pöschl-Teller potential hole
Convergence tests
Extension to variable effective mass
The double quantum well
Multiple quantum wells and finite superlattices
Addition of electric field
Quantum confined Stark effect
Field-induced anti-crossings
Symmetry and selection rules
The Heisenberg uncertainty principle
Extension to include band non-parabolicity
Poisson's equation
Self-consistent Schrödinger-Poisson solution
Computational implementation
Modulation doping
The high-electron-mobility transistor
Band filling
Diffusion
Introduction
Theory
Boundary conditions
Convergence tests
Constant diffusion coefficients
Concentration dependent diffusion coefficient
Depth dependent diffusion coefficient
Time dependent diffusion coefficient
!-doped quantum wells
Extension to higher dimensions
Impurities
Donors and acceptors in bulk material
Binding energy in a heterostructure
Two-dimensional trial wave function
Three-dimensional trial wave function
Variable-symmetry trial wave function
Inclusion of a central cell correction
Special considerations for acceptors
Effective mass and dielectric mismatch
Band non-parabolicity
Excited states
Application to spin-flip Raman spectroscopy
Alternative approach to excited impurity states
The ground state
Position dependence
Excited States
Impurity occupancy statistics
Excitons
Excitons in bulk
Excitons in heterostructures
Exciton binding energies
1s exciton
The two-dimensional and three-dimensional limits
Excitons in single quantum wells
Excitons in multiple quantum wells
Stark Ladders
Self-consistent effects
Spontaneous symmetry breaking
2s exciton
Strained quantum wells, V. D. Jovanovíc
Stress and strain in bulk crystals
Strain in quantum wells
Strain balancing
Effect on the band profile of quantum wells
The piezoelectric effect
Induced piezoelectric fields in quantum wells
Effect of piezoelectric fields on quantum wells
Simple models of quantum wires and dots
Further confinement
Schrödinger's equation in quantum wires
Infinitely deep rectangular wires
Simple approximation to a finite rectangular wire
Circular cross-section wire
Quantum boxes
Spherical quantum dots
Non-zero angular momentum states
Approaches to pyramidal dots
Matrix approaches
Finite difference expansions
Density of states
Quantum dots, M. Califano
0-dimensional systems and their experimental realisation
Cuboidal dots
Dots of arbitrary shape
Application to real problems
A more complex model is not always a better model
Carrier scattering
Fermi's Golden Rule
Phonons
Longitudinal optic phonon scattering of bulk carriers
LO phonon scattering of two-dimensional carriers
Application to conduction subbands
Averaging over carrier distributions
Ratio of emission to absorption
Screening of the LO phonon interaction
Acoustic deformation potential scattering
Application to conduction subbands
Optical deformation potential scattering
Confined and interface phonon modes
Carrier-carrier scattering
Addition of screening
Averaging over an initial state population
Intrasubband versus intersubband
Thermalised distributions
Auger-type intersubband processes
Asymmetric intrasubband processes
Empirical relationships
Carrier-photon scattering
Carrier scattering in quantum wires and dots
Electron transport
Introduction
Mid-infrared quantum cascade lasers
Realistic quantum cascade laser
Rate equations
Self-consistent solution of the rate equations
Calculation of the current density
Phonon and carrier-carrier scattering transport
Electron temperature
Calculation of the gain
QCLs, QWIPs, QDIPs and other methods
Optical properties of quantum wells, D. Indjin
Intersubband absorption in quantum wells
Bound-bound transitions
Bound-free transitions
Fermi level
Rectangular quantum well
Intersubband optical non-linearities
Electric polarisation
Intersubband second harmonic generation
Maximization of resonant susceptibility
Optical waveguides, C. A. Evans
Introduction to optical waveguides
Optical waveguide analysis
Optical properties of materials
Application to waveguides of laser devices
Multiband envelope function (k.p) method, Z. Ikoníc
Symmetry, basis states and band structure
Valence band structure and the 6 × 6 Hamiltonian
4 ×
valence band Hamiltonian
Complex band structure
Block-diagonalisation of the Hamiltonian
The valence band in strained cubic semiconductors
Hole subbands in heterostructures
Valence band offset
The layer (transfer matrix) method
Quantum well subbands
The influence of strain
Strained quantum well subbands
Direct numerical methods
Empirical pseudopotential theory
Principles and Approximations
Elemental Band Structure Calculation
Spin-orbit coupling
Compound Semiconductors
Charge densities
Calculating the effective mass
Alloys
Atomic form factors
Generalisation to a large basis
Spin-orbit coupling within the large basis approach
Computational implementation
Deducing the parameters and application
Isoelectronic impurities in bulk
The electronic structure around point defects
Microscopic electronic properties of heterostructures
The superlattice unit cell
Application of large basis method to superlattices
Comparison with envelope-function approximation
In-plane dispersion
Interface coordination
Strain-layered superlattices
The superlattice as a perturbation
Application to GaAs/AlAs superlattices
Inclusion of remote bands
The valence band
Computational effort
Superlattice dispersion and the interminiband laser
Addition of electric field
Application to quantum wires and dots
Recent progress
The quantum-wire unit cell
Confined states
V-grooved quantum wires
Along-axis dispersion
Tiny quantum dots
Pyramidal quantum dots
Transport through dot arrays
Anti-wires and anti-dots
Concluding Remarks
Materials parameters
References
Topic Index
Table of Contents provided by Publisher. All Rights Reserved.

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